How do you solve for r in #- \frac{59}{60} = \frac{1}{6} \(- \frac{4}{3} r-5 )#?

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Answer 1 · 2014-12-12T20:31:33

Answer: #r = 27/40#

Explanation:
We start with our equation:

#-59/60 = 1/6(-4/3r - 5)#

We can now multiply both sides of the equation by #6#:

#(-59* 6)/60 = -4/3r - 5#

We notice that #60 = 6*10# so we can cancel out the #6# on the left hand side:

#(-59*6)/(10*6) = -4/3r - 5#

#-59/10 = -4/3r - 5#

Now we can add #5# to both sides to further isolate r:

#-59/10 + 5 = -4/3r - 5 + 5#

#-59/10 + 50/10 = -4/3r#

#-9/10 = -4/3r#

And then multiply both sides by #3/4# to get the value of r:

#-9/10*-3/4 = -4/3r*-3/4#

#-9/10*-3/4 = r#

#27/40 = r#

#r = 27/40#

Checking work:

#-59/60 = 1/6(-4/3r - 5)#

#-59/60 = 1/6(-4/3*27/40 - 5)#

#-59/60 = 1/6(-108/120 - 5)#

#-59/60 = 1/6(-27/30 - 5)#

#-59/10 = (-27/30 - 5)#

#-59/10 + 5 = -27/30#

#(-59 + 50)/10 = -9/10#

#-9/10 = -9/10#